Automated Wing Internal Structure Placement Guided byFinite Element Analysis

Justin L. Clough∗ and Assad A. Oberai†University of Southern California, Los Angeles, CA, 90089

Andrew J. Zakrajsek‡

AFRL/RQHV, Wright-Patterson AFB, Dayton, OH, 45433

The global structural design layout is typically missing in the early conceptual phase ofaircraft design; the internal structure itself is usually left uninitialized until the externalgeometry of the vehicle is finished. This can lead to errors in the predicted performanceof the aircraft. This work details and demonstrates a program, GRASP, which automaticallydetermines the optimal structural layout of traditional components (ribs and spars) for usein this early design stage. A user needed to only provide a wing outer mold line, materialproperties, vehicle weight, and allowable wing tip deflection. A branch-and-cut style algorithmwas implemented to explore the design space of possible rib and spar configurations. Foreach configuration, a design flow of parametric geometry creation, discretization, and finiteelement analysis was performed automatically using all open source software packages. Thiswas demonstrated for a wing and other parameters representative of the X-15 aeroplane. TheGRASP program calculated a optimal initial design layout of 5 ribs and 2 spars in 139minutes; itevaluated a total of 11 different configurations and successively selected the one which loweredwing tip deflection. Future work includes adding a more representative loading conditions tomatch those seen in flight and methods to decrease program run time.

Nomenclature

GRASP = Guided Rib And Spar PlacementMER = Mass Estimating RelationsFE = Finite ElementAM = Additive ManufacturingOML = Outer Mold LineESP = Engineering Sketch Pad

IntroductionThe conceptual design of modern aerospace systems is grounded in various multi-disciplinary design processes.

These conceptual designs typically focus on the aerodynamic performance, weight assumptions, trajectory analysis,and overall ability of the system to meet the design requirements. A key discipline missing from the majority of earlyconceptual design, is the global structural design. This is due to the complex nature and knowledge required to designthe internal structural layout of a new aerospace system [1–3]. Compounding this complexity is the ever changingvehicle geometry during the conceptual design phase, mainly due to recent advances in parametric geometry. Dueto the early design fluidity, the conceptual structural design has been mainly incorporated in design loops throughmaterial selection and the resulting empirical Mass Estimating Relations (MERs) [1]. These relations are used untilthe conceptual design is nearly finalized, which then initializes the structural design. The structural design typicallystarts with rough hand calculations, up to Finite Element (FE) methods, and eventual structural testing. At this point inthe design cycle it is typically too late to greatly affect the overall system design [2]. Therefore, the final conceptual

∗PhD Student, Aerospace and Mechanical Engineering Department, 854 Downey Way, RRB 101.†Professor, Aerospace and Mechanical Engineering Department, 854 Downey Way, RRB 101.‡Research Engineer, Air Force Research Laboratory, AFRL/RQ Bldg. 45, 2130 Eighth Street, Wright-Patterson AFB, OH 45433.

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design can complicate the structural design and result in increased weight or reduced efficiency of the system. The earlyincorporation of structural design is important for understanding the proposed system’s feasibility, generating accurateweight predictions, assisting the multi-disciplinary design trade space exploration, and guiding the system to an optimalsolution.

To generate rapid conceptual design trades, the structural layout and design should mainly be automated at theconceptual level. Automated structural design and layout has mainly been researched in two separate thrusts: (1)topology optimization, and (2) automated conventional structural optimization and layout. Advanced topology methodshave been shown to produce optimal internal geometries with respect to minimizing stress, weight, and other keyvariables [4, 5]. While this research does show future benefit for the aerospace industry, it is also directly coupled to thecurrent state of Additive Manufacturing (AM). A few of the top research challenges for AM when focused on aerospacesystem structures are: understanding and predicting damage, machine to machine variability, print scale limitations,and cost of AM [6–8]. Until these areas of research are better understood, AM is not currently a viable solution fortraditional aerospace structures. With this understanding, this work focused on the near-term, benefits of automating thestructural layout process and incorporating the results early in the conceptual design. While the automated structurallayout can be considered a form of topology optimization, it will only be denoted as automated layout throughout thiswork.

Automating the structural layout process requires a specific and detailed focus on the design geometry, in addition tothe selection of a structural analysis method. Recent research is focusing on incorporating structural design earlier in thedesign loop through automated hand calculation methods [1]. This is aimed at incorporating initial structural designearly in the design loop without the need for structural expertise. Adding to this other research has suggested that dueto increased computational power, the inclusion of FE method is possible early in conceptual design loop [9]. Thereare benefits from incorporating the more detailed FE analysis early in the design loop, however, this also introducesnew challenges, like automatic mesh generation. This issue is mainly addressed within the design framework. Astructural optimization method was completed using FE analysis, automatic mesh generation, and a framework (python)environment [10]. The framework becomes extremely important for the incorporation of the structural design in themulti-disciplinary conceptual design loop. As the design and geometry change the structural design needs to adapt andchange. This can be completed using parametric geometry, so the FE method and structural layout update as the vehicledesign updates [11]. Using geometry as the center of an automated parametric design loop showed to be an importantstep for linking the structural design within the conceptual design loop [12, 13]. Therefore, to truly bring automatedstructural design and placement early in the design loop, there needs to be a focus on common design geometry acrossdisciplines and a framework capable of FE analysis. This leads to the ability to take a conceptual Outer Mold Line(OML) to an initial structural layout without the structural designer in the loop.

Completing the automatic structural layout at a conceptual level requires design knowledge held by structuralexperts. The vast majority of research in this area has looked at automatically laying out the structure by manuallyspecifying the number of supports throughout the structure. This method still requires an engineer in the loop duringthe conceptual design. The manual layout of the initial structure for the conceptual design takes time, however, needsto be completed to allow a starting point for the FE analysis. For this work an initial structural placement will becompleted using a branch-and-cut style algorithm [14]. This will work to initialize the structural design and allowvarying internal automated layouts to take place. The selection of the final automated layout can be performed followingdesign constraints and objectives similar to topology optimization (minimize stress, etc.). Therefore, an OML canbe entered into the loop, and the structural design model can continue to add supports while analyzing the structureto finalize an initial solution. Eventually, the goal would be to add an element of knowledge-based conceptual andpreliminary structural design practices to this placement model [15–17]. While this is outside the work presented here,this area can become extremely beneficial for future conceptual structural designs as an ability to acquire a faster andhigher fidelity automated conceptual structural design.

The work presented here has the goal of highlighting the most advantageous method to achieve early automatedstructural conceptual designs, within the multi-disciplinary design loop independent of direct structural designerexpertise. To accomplish this the automated layout process needs an OML input, design loads, and objective (i.e.,minimize wing deflection below an allowable amount). The automation framework then should be linked to the sameparametric geometry engine, a layout generation method, FE analysis, and a tailorable framework. The resulting workhighlights how an automated conceptual design framework was setup to automate a structure layout without any inputfrom the structural designer.

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MethodsThe goal was to develop an automated workflow to solve an optimal parametric structural layout problem. In this

problem, a user specifies a design constraint that must be satisfied, and a set of integer parameters that define thegeometry of the structure. The goal is to find an optimal value of these parameters that would achieve the designconstraint. In the specific problem considered, the design constraint is a bound on the maximum allowable tip deflectionof a wing under a prescribed loading, the integer parameters are the number of ribs and spars in the wing, and the goal isto find the smallest number of spars and ribs that would achieve the tip-deflection constraint.

In order to solve this problem, the workflow described in Figure 2 was developed. Here the first portion is a geometrycreation component, which given the value of the parameters of interest, generates the geometry of the structure. Thesecond component further processes this geometry and generates a FE mesh for it. The third component uses this meshto solve a structural analysis problem and evaluates the value of the design constraint. Once this workflow is established,it may be used to solve the optimal structural design problem using an appropriate integer programming algorithm.Since the focus of this paper is to demonstrate how this workflow can be established, a simple integer optimizationalgorithm, that is the branch-and-cut method, was used to solve this problem [14]. This algorithm proceeds as follows:

1) Start with an initial configuration that does not satisfy the design constraint.2) Increment each integer parameter by 1, and use the workflow to generate multiple designs and to determine the

design constraint for each design.3) If the design constraint is satisfied by one or more designs, the problem is solved.4) If no design satisfies the constraint, select the one that provided the largest drop in the constraint, and go to Step 2.

The different configurations formed the nodes of a tree which was traversed in a depth-first manner. An example of thistree is shown in Figure 1.

Initial Problem:1 Rib, 1 Spar

2 Ribs, 1 Spar 1 Rib, 2 Spar

2 Ribs,2 Spars

1 Ribs,3 Spars

Fig. 1 Example decision tree with configurations as nodes.

A python script, GRASP∗, (Guided Rib And Spar Placement) was written to implement the design flow logic and tooperate the branch-and-cut algorithm. This design flow is shown in Figure 2; it includes component creation, geometrymanagement and discretization, and the FE analysis.

Component Creation:• Read wing OML.• Create desirednumber of ribs.

• Create desirednumber of spars.

Geometry Managementand Discretization:• Read in wingcomponents.

• Label boundaries ofinterest.

• Discretize into amesh.

Finite Element Analy-sis:• Read in mesh.• Assign materialproperties andboundary conditions

• Solve fordisplacements.

Fig. 2 Automatic design flow logic and steps.

Templated base input files were created for use with each of the subprograms used at each step of the design flow. Thepython script edited the corresponding input file for the specific problem configuration. It then called each subprogramin the necessary order.

∗GRASP repository at github.com/JustinClough/grasp

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The script based geometry kernel Engineering Sketch Pad (ESP) was used to create a geometry of a problem ofinterest [18]. For this study, the base geometry was the right wing of the X-15, borrowed from [19]. This geometry wasthen populated with ribs and spars; these components each had a prescribed thickness. The ribs and spars were writtento disk and then read into Gmsh [20]. This software then joined all components together through boolean fragmentationand unions to form a single solid geometry. It then was used to produce a second order tetrahedral mesh discretizationof this geometry. The FE analysis software Albany [21] then read in this mesh, solved a linear elastic problem, andcalculated the deformation and stresses of the geometry in the wing under a predefined load condition. Each of thesedesign flow steps are described in detail in the following subsections.

Parametric Geometry with ESPTwo sets of two .udc files were written to allow a user to parametrically place ribs and spars for any wing shape.

A .udc file contains a user defined function. One of these files, make_rib.udc, allows the user to place a rib at aspecified percent-span. The other in this set is even_ribs.udc; this calls make_rib.udc to place a user definednumber of ribs evenly throughout the span of the wing. A similar set of programs were created for spar placement.

A templated input script was created and used for each problem configuration considered. The numbers of ribs andspars were automatically edited. Next, the ESP binary was called as a subprocess. The geometries created by thesescripts were then written to disk as .stp files [22]. Each component was written in its own .stp file. The genericmethod was rib_R.stp contained all geometric information of rib number R; spar_S.stp contained all geometricinformation of spar number S. When finished, the output was checked for errors.

Three main types of wing shapes were tested to verify the .udc files worked as expected. The three wing shapeswere Standard, Double Delta, and Double Dihedral. Examples of these shapes are shown in Figure 3.

(a) Standard. (b) Double Delta. (c) Double Dihedral.

Fig. 3 Geometries of the three base wing types.

The rib and spar file sets were then able to be read into Gmsh. The tessellation automatically performed by ESP was notused for the FE analysis.

Geometry Management and DiscretizationA template Gmsh script file was created and automatically edited for each problem configuration. The script first

read the first spar and rib from disk. It then used boolean fragmentation and unions to form a new single continuousvolume from the two components. The next component was then read from disk and added to the union in a similarmethod. This was repeated for all components until a single volume was formed that had all ribs and spars.

Boundaries of interest were then automatically found and labeled. This included the wing root surfaces and thewing underside. Each spar root surface was found by identifying the surface enclosed in a thin bounding box near thewing root and at the corresponding percent chord. The wing underside was determined as the surface with the lowestboundary. These surfaces were labeled such that boundary conditions could be applied during the FE analysis step.

The geometry was then discretized into second order tetrahedral elements. A size field was specified such that atleast two elements spanned any geometric feature.

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Finite Element ModelTwo template Albany input files were created and automatically edited for each problem configuration. The first file

dictated boundary conditions and linear algebra solver parameters. The second file specified material information suchas model type and properties.

A linear elastic material model was used. The user specified the Young’s modulus and Poisson ratio for the material.All components of the wing used the same material model and properties. The elements used were 10-node compositetetrahedrons [23]. These elements were chosen after testing in order to ensure that they did not suffer from shear lockingoften observed in some standard FE formulations.

All degrees of freedom on the wing root surface were assigned a homogeneous Dirichlet boundary condition. Theunderside of the wing was assigned a Neumann boundary condition of a uniform upward traction. The magnitude ofthis traction was calculated by distributing a user defined total weight over the lower surface area. This was to representthe lift from airflow over the wing.

Workflow DemonstrationWing tip deflection was brought below a prescribed allowable level using the GRASP program for a example aircraft.

The OML of the X-15 was used as the base wing geometry [19]. Material properties of Ti6Al4V were used; thesewere a Young’s modulus of 113.8 GPa and a Poisson’s ratio of 0.342 [24]. A weight of 123.0 KN, representing thefull weight of the X-15 [19], was distributed uniformly as an upward pressure over the bottom face of the wing. Thisapproximated the load of a 2G maneuver on the wing frame. The spars were created with thicknesses of 30 mm; ribshad a thickness of 5 mm. An allowable tip deflection of 5 cm was used.

ResultsImages showing the internal geometries created by the .udc files are shown for verification of expected function

behavior. This includes internal views for both the Double Delta and Double Dihedral wings. Images and plots from thetip deflection demonstration are presented as well. These include a surface plot tip deflection with respect to consideredconfigurations and images of meshes used for the FE model. Solution times and timing breakdowns are also shown.

Validation of .udc FilesThe .udc files were tested on the Double Delta and Double Dihedral wing types shown in Figure 3. Figure 4 shows

the variability of the number of internal components which can be placed. An isometric view of the internal componentsfor the Double Delta wing is shown in Figure 5; a similar view for the Double Dihedral is shown in Figure 6. Imagesshow components with zero thickness for clarity.

(a) Few internal components. (b) Mixed number of internal components. (c) Many internal components.

Fig. 4 Double delta wing with differing numbers of parametrically placed internal supports.

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(a) External view. (b) Top surface removed.

Fig. 5 Double delta wing with and without top surface to show geometries of the internal components.

(a) External view. (b) Top surface removed.

Fig. 6 Double dihedral wing with and without top surface to show geometries of the internal components.

Demonstration Of Full WorkflowA surface plot generated by computing the tip deflection for numbers of ribs and spars is shown in Figure 7. A spar

and rib thickness of 30 mm and 4 mm, respectively, was used along with the geometry and weight for the X-15. Thisshows the sensitivity of the deflection at the tip of the wing to various configurations of ribs and spars.

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68

24

68

10−3

10−2

10−1

100

SparsRibs

TipDeflectio

n(m

)

Fig. 7 Tip deflection with respect to numbers of ribs and spars.

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The maximum tip deflection was for the 1-rib, 1-spar configuration and was 14.6 meters. The minimum tip deflectionwas 5.9 mm for the 8-rib, 8-spar configuration.

A demonstrative problem was run to test the entire workflow. In this problem the goal was to find the integercombination of ribs and spars that produced a tip deflection for a X-15 wing less than 5 cm with the fewest numberof total components. The initial configuration was a wing with a single rib and spar. The skin of the wing was notmodeled; it was determined that it did not provide significant bending stiffness to the structure. The entire load on thewing, equal to 123.0 KN, was distributed uniformly on the lower surface of the ribs and spars.

The path selected by the optimization algorithm is shown in Table 1 and Figure 8. The algorithm reached theprescribed constraint in 5 steps. Each step required the generation of two configurations and the solutions of thecorresponding structural problems. The final configuration comprised of 5 ribs and 2 spars produced a tip deflection of3.62 cm. As shown in Figure 8, the algorithm added the second spar in the second step and thereafter always preferredadding a rib over another spar.

Table 1 Intermediate configurations and deflections.

Step Number Ribs Spars Displacement [mm]0 1 1 4040.01 2 1 966.72 2 2 345.53 3 2 137.04 4 2 66.35 5 2 36.2

1 Rib,1 Spar

2 Ribs,1 Spar

3 Ribs,1 Spars

2 Ribs,2 Spars

3 Ribs,2 Spars

4 Ribs,2 Spars

5 Ribs,2 Spars

4 Ribs,3 Spars

3 Ribs,3 Spars

2 Ribs,3 Spars

1 Rib,2 Spar

Fig. 8 Path taken by GRASP to build wing frame. Configuration that lowered tip deflection is circled at eachlevel.

The value of tip deflection at each step for the two configurations that were evaluated, one with an extra rib andanother with an extra spar, is shown in Figure 9. It was observed that except for the second step, the tip deflectionproduced by adding an extra rib was smaller than that produced by adding and extra spar.

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1 2 3 4 5

102

103

Step Number

TipDeflectio

n[m

m]

Tip Deflection At Each Step

Added RibAdded Spar

Fig. 9 Tip deflection with respect to the number of steps taken for adding either a rib or spar.

The total computer time required for generating and solving the two configurations at each step is shown in Figure10. The solution time grows by a factor of 10 between the first and the last step. This is because with each step asmore components are added to the model, the effort required to construct and mesh the geometry and then to solvethe corresponding FE problem increases. At each step the time required to solve the problem with an extra rib was21% to 32% more than the time required for the extra spar problem. This can be attributed to the extra effort requiredin meshing the thin region near the trailing edge. This plot also illustrates the advantage of using the branch-and-cutalgorithm over an exhaustive search; spanning the entire parameter space would become prohibitive with the increasingnumber of components in the latter approach.

1 2 3 4 50

500

1,000

1,500

2,000

Step Number

Time[s]

Solution Time At Each Step

Added RibAdded Spar

Fig. 10 Time to calculate solution for each configuration with respect to the number of steps taken for addingeither a rib or spar.

The number of finite elements generated for the two configurations at each step of the algorithm are shown in Figure11. These increase by 5,000 to 10,000 with each step and rise to a total of 50,0330 for the final evaluated configuration.On average, spars and ribs required roughly 9000 and 5000 elements to model, respectively.

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1 2 3 4 5

2

3

4

5

·104

Step Number

Num

bero

fElements

Number Of Elements At Each Step

Added RibAdded Spar

Fig. 11 Finite elements in each mesh for each configuration compared to the number of steps taken foradding either a rib or spar.

Table 2 provides a break-down of the computational time spent in the three main components of the workflow:geometry creation in ESP, geometry processing and mesh generation in Gmsh, and FE analysis in Albany. For the initialconfiguration, the time spent in Gmsh and Albany was similar and was three times the time spent in ESP. However,for the final few configurations the situation was reversed; here most of the time was spent in combining the differentcomponents and then meshing them in Gmsh. Remarkably the time required for the FE analysis was less than a tenth ofthis time. This may be attributed to the advanced solvers and preconditioners used within Albany [21]. The programtook a total of 139 minutes to run on a Linux workstation with a i5-7400 CPU which had a clock speed of 3 GHz.

Table 2 Time in each portion of the design flow throughout evaluated configurations. All times in seconds.

Step Number Ribs Spars Geometry Creation Geometry Management and Discretization FE Analysis0 1 1 13 39 391 2 1 14 66 892 2 2 14 287 693 3 2 16 656 914 4 2 16 1206 1125 5 2 16 1871 122

In Figure 12, the geometry and the mesh at each step are plotted; in Figure 13 the deformed shape of the configurationis shown. In this figure, for each configuration, the surface is colored with the magnitude of displacement. The maximumdeflection occured at the tip of the spar closer to the leading edge, and that with each new rib that was added themagnitude of this displacement, as well as the difference between the tip deflection of this spar and the one downstreamof it, reduced.

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(a) Step 0: 1 Rib, 1 Spar. (b) Step 1: 2 Rib, 1 Spar.

(c) Step 2: 2 Rib, 2 Spar. (d) Step 3: 3 Rib, 2 Spar.

(e) Step 4: 4 Rib, 2 Spar. (f) Step 5: 5 Rib, 2 Spar.

Fig. 12 Meshes used at different solution steps.

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(a) Step 0: Scale of 0.1. (b) Step 1: Scale of 1.0.

(c) Step 2: Scale of 1.0. (d) Step 3: Scale of 5.0.

(e) Step 4: Scale of 10. (f) Step 5: Scale of 20.

Fig. 13 Mesh at each step with displacement magnitude contour plot and deformed with the displacementvector; scale factors used to show deflections.

Discussion and Closing RemarksThe GRASP program was able to solve an optimal parametric structural layout problem by automatically creating

an initial frame design. A user specified design constraint, maximum allowable wing deflection, was satisfied bydetermining the integer numbers of ribs and spars to populate the wing frame for a demonstrated vehicle. A simplifiedversion of the branch-and-cut method was used to step through possible configurations. For each configuration, a designflow consisting of component creation, geometry discretization, and a FE analysis was executed.

The components of the wing frame were created using the parametric, script-based, geometry kernel ESP. Each

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component was written to disk and then read into Gmsh automatically. The components were then unioned together toform one continuous volume which represented the wing frame. Boundaries of interest were tagged and the volume wasdiscretized into a FE mesh which was written to disk. This mesh was then read into Albany where boundary conditionsand material properties were assigned. The FE problem was then solved for nodal displacements.

The demonstration shows that the GRASP program was able to create a design for the frame of a wing OMLautomatically in approximately 2 hours. In this time it considered 11 different configurations and successively chose theone which lowered tip deflection. This was done using all open-source software packages.

This work demonstrates a viable method to bring structural layout into the initial design phase for aircraft. It doesso without the need for a structural design specialist present. This will benefit the air vehicle design community byintroducing greater modeling accuracy earlier in the design process. In turn this will lead to aircraft designs whichmore efficiently meet their design criteria. Additionally, layouts generated using GRASP rely on traditional and testedmanufacturing methods.

Future WorkPossible improvements would include allowing for different materials throughout the wing, modeling the wing skin

with stringers, and testing under more load cases. These additions would allow for more accurate modeling of the wingin use.

Allowing for different components to have different material properties would generalize the given method. Somebut not all wing constructions use the same material throughout the wing. For example, the X-15 used both Inconeland Titanium alloys in its wing construction, [25, 26], whereas a commercial Cessna uses the same Aluminum alloythroughout the wing, only differing by temper [27]. Additionally, different material models could be used on differentcomponents. These models would include the pertinent physical behavior needed to understand the performance of thedesign. Including the wing skin and stringers would also increase the general accuracy of the model. This would beespecially important for more complex load cases where the stringers and skin must distribute the aerotractions to theribs and spars. Lastly, more complex load cases could be created and designed for to better represent those in flight.

The GRASP software can also be made faster by a few methods. First, configurations can be processed in parallel;this would decrease the total solution time to near half. Second, both Gmsh and Albany are able to operate in parallel[20, 21]. Calling these application with parallel resources would also decrease the time to solve each configuration.Finally, each step of the design flow shown in Figure 2 starts and end with reading a writing to the disk. Processing fullyin memory without the file input/output would also decrease the total time to calculate solutions.

AcknowledgmentsThe authors thank the DoD Science, Mathematics, And Research for Transformation (SMART) Scholarship for

Service Program which sponsored this work.

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